- #1

byte

- 4

- 0

## Homework Statement

In a balanced three-phase wye-wye system, the source is an abc-sequence set of voltages and V_an = 120e^(i30°) V rms. The power absorbed by the load is 3435 W and the load impedance is 10 + j2 Ω. Find the two possible line impedance if the power generated by the source is 3774 W. Which line impedance is more likely to occur in an actual power transmission system?

Z_line = ?

Z_load = 10+j2 ohm

P_load = 3435 W

P_source = 3774 W

V_s = 120e^(i30°) V rms

## Homework Equations

V_an = I_aA (10 + j2 + Z_line)

P_s = V_an * I_aA cos θ / sqrt(3)

## The Attempt at a Solution

I can't seem to figure out a way to solve for any particular variable... I can find that the power of the line, P_line = 339 W, but that's about as far as I can get. The line impedance appears to be solved by:

Z_line = V_an - I_aA (Z_load) / I_aA

(derived from first relevant eq.)

But the current isn't given, and if I derive current I_aA from second relevant equation, then I don't know cos θ. The fact that there is a cos θ, it does make sense that there would be two valid line impedances.

Any thoughts?